Direct Measurement of Interface Roughness in QCL Materials Grown by MOCVD Matthew R. Wood 1, Federico Lopez 1, Michael Weimer 1, & Claire F. Gmachl 2 1 Department of Physics & Astronomy, Texas A&M University 2 Department of Electrical Engineering, Princeton University NSF ERC Cooperative Agreement EEC 0540832 Special thanks to C. Caneau, Corning Incorporated for the sample used in this study
Quantum Cascade Laser Conduction Band Profile vs Growth Direction barrier CBE not to scale 3 2 1 hv hv E hv k z well CBE
Quantum Cascade Laser Conduction Subband Energy vs In Plane Momentum intersubband lasing intersubband scattering 1 2 3 1 2 3 hv ~ 250 mev q ~ 0.05 Å -1 ( smooth ) planar interfaces ( rough ) non planar interfaces
Elastic Scattering 2 D Plane Waves q = κ - κ e i k κʹ ρ r r x e i k κ ρ r κ ρ H pert (ρ) e i κ ρ 2 k r r e i k ʹ r r y z Power Spectral Density Autocorrelation Function
Elastic Scattering Stochastic Well Width Fluctuations q = κ - κ e i k κʹ ρ r r x e i kκ ρr h(r) h(r) r y z δe(ρ) = δe n r δl w h(ρ) r κ ρ H (ρ) e i κ ρ k r r 2 pert e i k ʹ r e i k ʹ r κ ρ h(ρ) e i κ ρ 2 k r r
Device Characterization Cross Sectional TEM 4 stages of a Quantum Cascade Laser 55 nm InGaAs InAlAs [110] [001] TEM image courtesy Dr. Nan Yao, Princeton University
Device Characterization Cross Sectional STM 50 mm [110] not to scale (001) [110]
InAlAs / InGaAs Superlattice Device Scale STM Survey Period 15 Period 15 ] nm 0] [11 01 0 [0 (110) 10 [11 0] (110) 2.5 V 200 pa [0 01 ]
InAlAs / InGaAs Superlattice Interface Identification grey level probability well barrier s threshold 20 nm ] 10 [1 01 [0 ] InAlAs InGaAs grey level intensity
InAlAs / InGaAs Superlattice Interface Identification grey level probability well barrier s threshold 20 nm ] 10 [1 01 [0 ] InAlAs InGaAs grey level intensity
Elastic Scattering Gaussian Well Width Fluctuations e i k ʹ r κ ρ h(ρ) e i κ ρ 2 k r r = Δ 2 Λ 2 exp Λ2 kκ kʹ 2 κ 2 h(ρ) r h( ρ rʹ ) = Δ 2 exp ρ r r ʹ 2Λ 2 ρ 2 D rms amplitude L correlation length ensemble average
Interface Roughness Observed Autocorrelation Function [110] interface profile [110] interface profile roughness autocorrelation 1.0 InGaAs on InAlAs = 0.89 ± 0.01 ML InAlAs on InGaAs = 0.74 ± 0.01 ML InGaAs on InAlAs = 0.87 ± 0.01 ML InAlAs on InGaAs = 0.77 ± 0.01 ML 0 0 20 0 20 in plane separation ( a 110 ) in plane separation ( a 110 )
Interface Roughness Effect on Intersubband Lifetime single scale, isotropic autocorrelation τ 1 IFR = 2π m* 3 Δ2 δu 2 f 3 (z j ) f 2 (z j ) j ( ( )) { } 2 Λ 2 exp Λ 2 q 2 2 IFR = interface roughness, i = length scale index, j = interface index du = band offset, f = envelope function, q = momentum transfer Y. Chiu, Y. Dikmelik, P. Q. Liu, N. L. Aung, J. B. Khurgin, and C. F. Gmachl, Applied Physics Letters 101, 171117 (2012)
Interface Roughness Effect on Intersubband Lifetime multi scale, anisotropic autocorrelation τ 1 IFR = m * 3 Δ2 δu 2 f 3 (z j ) f 2 (z j ) j * * { } 2 i i ( ) ( 2 P(Λ ij [110] ) Λ ij [110] exp Λ ij [110] q 2 [110] 2 ) ( ) ( 2 P(Λ ij [110] ) Λ ij [110] exp Λ ij [110] q 2 [110] 2 ) IFR = interface roughness, i = length scale index, j = interface index du = band offset, f = envelope function, q = momentum transfer
Interface Roughness Scattering Intersubband Wave Vector Dependence [110] plane waves [110] plane waves InGaAs on InAlAs InGaAs on InAlAs log matrix element 2 InAlAs on InGaAs q InAlAs on InGaAs q momentum transfer ( Å 1 ) momentum transfer ( Å 1 )
Interface Roughness Scattering Intersubband vs Intrasubband intersubband scattering intrasubband scattering 1 2 3 1 2 3 q ~ 0.05 Å -1 q 0.02 Å -1 rough interfaces rough interfaces
Interface Roughness Scattering Intrasubband Wave Vector Dependence [110] plane waves [110] plane waves InGaAs on InAlAs InGaAs on InAlAs log matrix element 2 q InAlAs on InGaAs q InAlAs on InGaAs momentum transfer ( Å 1 ) momentum transfer ( Å 1 )
Summary Problem interface roughness limits QCL performance Approach real space visualization with STM heterojunction specific ( growth order asymmetry ) cross section specific ( growth plane anisotropy ) Observed Roughness Properties multi scale gaussian autocorrelation short range alloying intermediate range clustering long range terrace island structure growth order dependent at intermediate and long ranges Predicted Roughness Scattering strongly growth order asymmetric at wavevectors of device interest ( for growth order symmetric envelope functions ) Bottom Line InGaAs on InAlAs dominates intersubband ( and intrasubband ) lifetime ( absent compensating envelope function amplitudes )